# Performance Analysis of Plug-and-Play ADMM: A Graph Signal Processing Perspective

arXiv: https://arxiv.org/abs/1809.00020 · HTML: https://mlsanity.com/paper/1809.00020/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2018.

## Built on by (most cited first, 13 of 13)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization](https://mlsanity.com/paper/2201.13256/) (2022)
- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [Fixed-Point and Objective Convergence of Plug-and-Play Algorithms](https://mlsanity.com/paper/2104.10348/) (2021)
- [Graph Signal Restoration Using Nested Deep Algorithm Unrolling](https://mlsanity.com/paper/2106.15910/) (2021)
- [Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysis](https://mlsanity.com/paper/2310.00133/) (2023)
- [Decoupling Training-Free Guided Diffusion by ADMM](https://mlsanity.com/paper/2411.12773/) (2024)
- [PnP-CM: Consistency Models as Plug-and-Play Priors for Inverse Problems](https://mlsanity.com/paper/2509.22736/) (2025)
- [Analysis of function approximation and stability of general DNNs in directed acyclic graphs using un-rectifying analysis](https://mlsanity.com/paper/2206.05997/) (2022)
- [Radio Map Estimation via Latent Domain Plug-and-Play Denoising](https://mlsanity.com/paper/2501.13472/) (2025)
- [Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework](https://mlsanity.com/paper/2603.10281/) (2026)
- [A Unified Plug-and-Play Algorithm with Projected Landweber Operator for Split Convex Feasibility Problems](https://mlsanity.com/paper/2408.12100/) (2024)

## Abstract (arXiv)

The Plug-and-Play (PnP) ADMM algorithm is a powerful image restoration framework that allows advanced image denoising priors to be integrated into physical forward models to generate high quality image restoration results. However, despite the enormous number of applications and several theoretical studies trying to prove the convergence by leveraging tools in convex analysis, very little is known about why the algorithm is doing so well. The goal of this paper is to fill the gap by discussing the performance of PnP ADMM. By restricting the denoisers to the class of graph filters under a linearity assumption, or more specifically the symmetric smoothing filters, we offer three contributions: (1) We show conditions under which an equivalent maximum-a-posteriori (MAP) optimization exists, (2) we present a geometric interpretation and show that the performance gain is due to an intrinsic pre-denoising characteristic of the PnP prior, (3) we introduce a new analysis technique via the concept of consensus equilibrium, and provide interpretations to problems involving multiple priors.